Cool…I put in a CR2330 (available at Batteries Plus shops, for those forum members in the US), and I was hoping that would be fine, although I see that Italo said a couple years ago to avoid the CR. I was told that the BR and CR were essentially interchangeable. You can use a CR in place of a BR, but you cannot use a BR in place of a CR–so said the person I spoke with at Batteries Plus.
It does seem to have solved the internal memory checksum error problem. I had to reset the RAM when I first turned on the Eclipse after installing the new battery. Fingers crossed all is well, but it appears to be.